Solid State Physics Byungwoo Park Department of Materials Science and Engineering Seoul National University

Transcription

1 Solid State Physics Byungwoo Park Department of Materials Science and Engineering Seoul National University

2 Types of Crystal Binding Kittel, Solid State Physics (Chap. 3) Solid State Physics Jongmin 2

3 Cohesive Energies of Elements Kittel, Solid State Physics (Chap. 3) Solid State Physics BP 3

4 Bond Energies for Single Covalent Bonds Kittel, Solid State Physics (Chap. 3) Solid State Physics BP 4

5 Bond Energy Lange s Handbook of Chemistry Solid State Physics BP 5

6 Fractional Ionic Character of Bonds in Binary Crystals Kittel, Solid State Physics (Chap. 3) Solid State Physics BP 6

7 Optical Phonon vs. Acoustical Phonon parabolic Kittel, Solid State Physics (Chap. 4) Solid State Physics BP 7

8 Phonon: Density of State Density of State for Phonon: - The vibrations of the lattice (heat) - Given frequency (energy), possible phonon mode - Heat capacity D(w): density of state <n> : Plank distribution C v = (δu/δt) v Debye Frequency / Debye Temperature Kittel, Solid State Physics (Chap. 5) Solid State Physics Yejun 8

9 Heat Capacity Debye Approximation Heat Capacity Kittel, Solid State Physics (Chap. 5) Solid State Physics Jongmin 9

10 Density of Occupied State for Electrons E = (ħk) 2 /2m k = (3π 2 n/v) 1/3 D(E) = dn/de = V/2π 2 (2m/ħ) 3/2 E 1/2 Density of occupied state = D(E)f(E) = 1/[exp{(E-E F )/kt}+1] V/2π 2 (2m/ħ) 3/2 E 1/2 DOS(E) = D(E) ~ E 1/2 3-dimension D(E) 1-dimension E Kittel, Solid State Physics (Chap. 6) Solid State Physics Yejun 10

11 Electrical Conductivity K(t)-k(0) = -eet/ħ ; B = 0 Electrical conductivity: σ = ne 2 τ/m τ: collision time = neμ At 300 K, lattice phonon At 4 K, imperfection Phonon e Trap Impurity or Vacancy e Blocking Au 4.55 (ohm cm) -1 Pt 0.96 (ohm cm) -1 Ru 1.35 (ohm cm) -1 Al 3.65 (ohm cm) -1 Kittel, Solid State Physics (Chap. 6) Solid State Physics Yejun 11

12 Electron-Electron Collision: Negligible Conduction electrons, although crowded together by only 2 Å, travel long distances between collisions. why? Conservation of energy + Conservation of momentum ~k B T/ε F The mean free path for electron-electron collisions is much longer than the mean free path for electron-phonon collisions at ~300 K. Kittel, Solid State Physics (Chap. 14) Solid State Physics Jongmin 12

13 Electronic Structure of AlPO 4 : Band Structure Fermi level Bandgap: 5.71 ev Bandgap: 6.32 ev Bandgap: 4.01 ev - Structural transformation under pressure W. Y. Ching and Paul Rulis, University of Missouri-Kansas City Physical Review B (2008) Solid State Physics Yejun 13

14 Electronic Structure of AlPO 4 : Absorption Indirect Real dielectric function Imaginary dielectric function Absorption W. Y. Ching and Paul Rulis, University of Missouri-Kansas City Physical Review B (2008) Solid State Physics Yejun 14

15 Transparent Conducting Oxide (TCO) Conduction band In 0.96 Sn 0.04 O 1.5+δ Semiconducting Behavior Fermi level ~3.6 ev Metal-Like Behavior In 0.96 Sn 0.04 O 1.5-δ Valence band Reduction process (7% H 2 / 93% N 2 ): Removal of excess oxygen Solid State Physics Yejun K. R. Poeppelmeier s Group, Northwestern University Chem. Mater. (2002) 15

16 Energy Levels of Free Electron in a 1-D Box Kittel, Solid State Physics (Chap. 6) Solid State Physics Jongmin 16

17 Excitons in Nanoscale Systems Si CdS 14.7 mev 29.0 mev Exciton Binding Energy G. D. Scholes, Toronto University Nat. Mater. (2006) Solid State Physics Jongmin 17

18 Quantum Confinement W. E. Buhro, University of Washington Nat. Mater. (2003) Solid State Physics Jongmin 18

19 Frequency Dependence of Polarizability Kittel, Solid State Physics (Chap. 16) Solid State Physics Jongmin 19

20 Dielectric Function of Free-Electron Gas (Plasmon) - Plasma: a medium with equal concentration of positive and negative charge, of which at least one charge type is mobile. Motion of a free electron in an electric field (assumption: long wavelength dielectric response, ) ( ) ħω p = 16 ev for Au Kittel, Solid State Physics (Chap. 14) Solid State Physics Jongmin 20

21 Dispersion Relation for Transverse Electromagnetic Wave Kittel, Solid State Physics (Chap. 14) Solid State Physics BP 21

22 Surface Plasmon of Nanoparticles Luis M. Liz-Marzan, UniVersidade de Vigo, Langmuir (2006) Solid State Physics Jongmin 22

23 Surface Plasmon of Nanoparticles - Alloying - The electric field of the incoming radiation induces the formation of a dipole in the nanoparticle, and there is a restoring force that tries to compensate it. - Unique resonance frequency matches this electron oscillation within the nanoparticle. - Tuning the surface-plasmon energy by alloying. Luis M. Liz-Marzan UniVersidade de Vigo, Langmuir (2006) Solid State Physics Jongmin 23

24 Surface-Plasmon Enhanced Photoluminescence Prof. Harry Atwater, Caltech Nano Lett. (2005) Solid State Physics BP 24

25 Color of Metal Metal 의 color 에영향을주는요인 1. Free electron (bulk plasmon): Metal 의 free electron oscillation 에의해 bulk plasmon 에너지보다작은에너지를가지는빛은 reflect 됨. 대부분의 metal 이가시광에너지보다큰 bulk plasmon 에너지를가지고있기때문에 reflect 된가시광으로인해기본적으로금속광택을띠게됨. 2. Interband absorption: Metal 이빛과 interaction 을하려면같은밴드내에서는 momentum conservation 을만족시키지못하기때문에, 다른 band 로의 electron transition 이일어나야함. 이때일어날수있는 transition 은두가지 case 가있음 : (1) Fermi level 근처의 conduction electron 이더높은위치에있는에너지밴드로이동 (2) 아래쪽레벨에있는밴드에차있는 electron 이 conduction band 쪽으로이동 Ashcroft, Solid State Physics Solid State Physics Jongmin 25

26 Color of Metal Cu Band Structure Real band structure Fermi level 약간아래쪽에존재하는 Cu metal 의 d band 로인해아래쪽그림에없던밴드들이형성된것을확인할수있음. Absorption 이일어날수있는경우 : (1) 4 ev d band (2) 2 ev (2) 2 ev (1) 의경우 Fermi level 근처의 conduction electron 이더높은위치에있는에너지밴드로이동하는것. Free electron model (2) 의경우아래쪽레벨에있는밴드에차있는 electron 이 conduction band 쪽으로옮겨오는것. (2) 의경우가에너지가더작으므로 2 ev 정도부터흡수가일어나게됨. Ashcroft, Solid State Physics Solid State Physics Jongmin 26

27 Color of Metal Imaginary Dielectric Constant 아래그림은 Cu 와 Ag 의 imaginary dielectric constant - Cu 경우윗장의밴드구조에의해 2 ev 부터흡수가일어나기때문에낮은쪽에너지의색인붉은빛을띠게됨. - Ag 경우이러한흡수가 4 ev 에서일어나기때문에 visible 영역에영향을주지않아투명한광택색으로보이게됨. Ashcroft, Solid State Physics Solid State Physics Jongmin 27

28 Work Function Kittel, Solid State Physics (Chap. 17) Solid State Physics BP 28

29 Work Function (not real) Ashcroft, Solid State Physics Solid State Physics BP 29

30 Double Layer Work Function Ashcroft, Solid State Physics Solid State Physics BP 30

31 Potential Profile Across the Double Layer Bard, Electrochemical Methods Solid State Physics BP 31

32 Helmholtz Layer and Diffuse Layer Bard, Electrochemical Methods Solid State Physics BP 32

33 Standard Electrode Potentials Solid State Physics BP Bard, Electrochemical Methods (Appendix) 33